He also unified the field of algebraic number theory with his 1897 treatise Zahlbericht (literally "report on numbers").

Famous for his ability to make discoveries in various mathematical fields, Hilbert went on to provide the first correct and complete axiomatization of Euclidean geometry to replace Euclid's axiomatization of geometry, in his 1899 book Grundlagen der Geometrie ("Foundations of Geometry").

He also laid the foundations of functional analysis by studying integral equations and Hilbert spaces.